I switched from Chrome to Firefox because of font support for specific languages, namely Asian languages. In Chrome, you cannot specify a certain font for a certain language as you can with Firefox. By default, both Chrome and Firefox display Sinitic and Japanese languages with MS Mincho, which leaves ugly unreadable characters at small font sizes and incorrect characters for some CJK characters:
Specifying Meiryo for Japanese in Firefox gives wonderful, anti-aliased text with properly shown characters for Japanese:
Characters used in Japanese are also different than those used in Chinese, so it's also important to assign fonts specific for the language.
Other than the aforementioned off-topic level of customization and the ability to let Firefox not save history, I think I'd go with Chrome. The above is the sole reason I use Firefox.